Answers

1. Answer:

   a² + b² = 25/2

   Step-by-step explanation:

   a² – b² = 12…….eq(1)

   (a – b)² = 9……..eq(2)

   From eq(2),

   (a – b)² = 9

   (a – b) = √9

   (a – b) = 3………eq(3)

   Making “a” subject formula in eq(3), we have

   a = b + 3…………eq(4)

   Substituting eq(4) into eq(1)

   a² – b² = 12

   (b + 3)² – b² = 12

   (b+3)(b+3) – b² = 12

   9+3b+3b+b²–b² = 12

   9 + 6b + 0 = 12

   6b = 12–9

   6b = 3

   b = 3/6

   b = 1/2

   To find “a” from eq(4), when b=1/2

   a = b+3

   a = 1/2 + 3

   a = 7/2

   Therefore,

   a² + b² = (7/2)² + (1/2)² = 25/2

   To check if the values of “a” and “b” is correct, from eq(1) and eq(2)

   a² – b² = (7/2)² – (1/2)² = 12

   (a–b)² = (7/2 – 1/2)² = 9

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